Review 425
Fast-folding experiments and the topography of protein folding energy landscapes PG Wolynes’, Z Luthey-Schultenl and JN Onuchic*
The rapid folding of certain proteins can be described Introduction theoretically using an energy landscape in the shape of a For those who appreciate the beauty of the architecture of folding funnel. New techniques have allowed the examination folded proteins it is amazing to find that such complex of fast-folding events that occur in microseconds or less, and structures can be formed spontaneously in biologically have tested the predictions of the theoretical models. short times, although doing so is clearly an evolutionary necessity. In human affairs, complex organized structures Addresses: ‘School of Chemical Sciences, University of Illinois, have always been made by a series of individually simple Urbana, IL 61801, USA and 2Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA. steps. A similar picture of the folding process seemed to emerge from the classical kinetic studies of folding on time Chemistry & Biology June 1996,3:425-432 scales greater than a few milliseconds [l]. But it was real- ized that, particularly for smaller proteins, folding could 0 Current Biology Ltd ISSN 1074-5521 occur far more rapidly and without a requirement for this discrete stepwise assembly. This led to a view of protein folding based on a statistical mechanical characterization of the energy landscape of a folding protein ([Z] and refer- ences therein), and this viewpoint has received consider- able support from computational studies of model proteins [3-81. With this new perspective it becomes clear that we will only be able to directly unravel the basic mechanisms of biomolecular self-organization and measure the topogra- phy of the folding-energy landscape with a new generation of experiments using relatively newer techniques that are capable of monitoring protein folding on shorter time scales (lasers [9-131, NMR [14-191, ultrafast mixing [ZO] and protein engineering [21,22]). This review highlights a remarkable fast folding experiment described in this issue by Mines et al! [23], who show experimentally a regularity in the folding of two proteins that is expected from a statis- tical description based on the landscape theory. We first discuss the theoretical descriptions of rapid protein folding before exploring to what extent the experiments of Mines et all, and the increasing number of other recent fast folding experiments, support this description. Finally, we consider what the two fields have taught us so far about folding and the energy landscape.
The folding funnel The energy-landscape theory of folding starts with the view that folding kinetics are best considered as a progres- sive organization of an ensemble of partially folded struc- tures (Fig. l), rather than a serial progression between intermediates. Thus, to understand kinetics one must statistically characterize the number and the distribution of free energies of the members of an ensemble of protein molecules that have partial order. A few collective reaction coordinates or order parameters should suffice to organize the description of the energy landscape. In contrast to most organic chemistry reactions, where the reaction coordinates describe a single structure, here they are collective coordi- nates characterizing an ensemble of structures as in elec- tron transfer [24,25]. The search through these very large 426 Chemistry & Biology 1996, Vol3 No 6
stabilize correct (native) interactions, on average, more than one expects by chance. We thus say that fast-folding pro- teins satisfy the principle of minimal frustration [28]. On a global level, the landscape must resemble a funnel ([29-311 and J.N.O., P.G.W., Z.L.-S. & N.D. Socci, unpublished data) (Fig. 2). As a folding reaction coordinate approaches its native value, the peak in energy distribution of the ensemble of conformations shifts to a lower value, as shown in Figure 3. The mean energy of structures in the funnel goes down as the ensemble approaches the native state. Simultaneously the number of conformations decreases, reflecting a loss of configurational entropy. (The entropy of the solvent, so important for the hydrophobic force, is included in the solvent average (free) energies used in the statistical distributions characterizing the landscape.) The
Figure 2
Beginning of helix formation and collapse
%Biology, 1996
Network of conformational changes occurring in the ensemble of conformations for a protein as it folds to the native structure. The folding reaction coordinate Q is the average fraction of native contacts in members of the corresponding ensembles. The conformations in the transition state ensemble have a Q-value of -0.6. The intermediate structures are obtained from computer simulations of a four helix bundle with varying degrees of native character. By organizing the states by energy and CI instead of the specific intermediates, a funnel description of the folding process shown in Figure 2 is obtained. (The simulations shown here are based on associative memory Hamiltonian structure prediction algorithms and show diminished helicity at low Q.)
number of configurations may present difficulties as Transition state a = 0.6 pointed out by Levinthal years ago [26,27]. Even the protein conformations with given amounts of partial order have various energies that must be described by a distribu- tion [28]. This give rise to what is called a ‘rugged energy Discrete folding intermediates landscape’, because many non-native interactions can exist I in a (partially) disordered protein structure and these can Native structure 0 Chemistry % Biology, 1996 be either favorable or non-favorable energetically. Confor- mational transitions from the deeper energy states in an The schematic funnel for a 60-amino-acid helical protein as obtained ensemble must typically surmount an energy barrier deter- from the corresponding-states principle analysis [30] with the 27-mer mined both by this energetic ruggedness, AI@, and any lattice model. The positions of the molten globule states, the transition barriers provided by stereochemical constraints inherent in state ensemble, and the local glass transition (the point at which the polypeptide backbone. discrete trapping states emerge) are shown as a function of the order parameters: fraction of native contacts 0, the solvents averaged energy E, and the configurational entropy S, which are drawn to scale. The ruggedness of the landscape is reflected in the kine- The stability gap SE, quantitates the specificity of the native contacts. tics of escape from transient conformational traps. Fast The ruggedness of the landscape A& determines the local barriers, but folding would be impossible on an entirely rugged land- its value is not the conformational diffusion activation height, which is E, - 7&T{. kB is the Boltzmann constant, Tf is the folding temperature, scape, which is called a completely frustrated landscape. is the energy of the native structure. Fast folding is only possible because of guiding forces that and Enat Review Fast folding Wolynes et al. 427
Figure 3 collective reaction coordinates such as degree of collapse and local secondary structure has been recently deve- (a) . loped (Z.L.-S., B.E. Ramirez & P.G.W., unpublished data) a=o.z (Fig. 4). In this multidimensional picture the basic scenarios 4 SE, for folding remain the same, although new characteristic Log n(E) energies such as entropy diminution and energy loss upon collapse are needed to set up the correspondence. Fast Folded folding experiments will allow the characterization of these important parameters, which determine a major part of the entropy loss, ultimately leading to folding. (W E t t a=05 The dominant dependence of folding on the stability gap (the difference in stability between folded and unfolded states) is strongly supported by the experiments of Gray, Winkler and colleagues [l&23]. Global changes to the
Figure 4 Logn(E)E , a=i.o
Single kinetic step
Log n(E)
Free energy of the specified ensemble
Histograms of protein configurational states at various stages of folding. (a) Collapsed phase with Q = 0.2. (b) Transition state with C = 0.6 near the middle of the funnel. (c) Native state with 0 = 1 .O. In any given folding event, the protein molecule passes through intermediate Q states. In a type I folding, however, no significant population is trapped in these states, which are never substantially occupied kinetically. For downhill folding on fast time scales, these intermediate states may be sufficiently populated to be observed directly in the new fast-folding experiments. The y-axis is the logarithm of the number of configurations, and the x-axis is the free energy of a Molten 1 particular configuration averaged over the solvent. Native state globule 1 mean energy loss down the funnel gives an additional energy parameter characterizing the landscape topography, the stability gap 6E,. The configurational entropy loss, the third significant parameter, is called the Levinthal entropy (S,) as it is simply a logarithmic measure of the vastness of the configuration space of the biomolecule [30,32]. The fact Fraction native contacts, Q that the landscape can be described by these very few para- meters (SE,, S,, and AE) allows us to use a law of corre- The multidimensional aspect of the free-energy surface. The average free energy of the ensemble (as opposed to that of an individual sponding states (which uses scaling of certain known structure as shown in Fig. 2) is shown here as a function of the fraction parameters to directly compare two different proteins) to of native contacts, Q, and total contacts. The free energies include the understand the important characteristics of the funnel land- configurational entropy counting the number of states with a particular scape for real proteins by investigating analytical models value of the collective coordinates. The surface is plotted using the and lattice simulations [30]. This correspondence, and the analytical fit of Plotkin et al. [381, but the specific landmark values of Q are taken from the simulation results. At T, we see two distinct minimal quantitative one-dimensional funnel picture shown in free energy ensembles: one (red) specifying the molten globule, the Figure 2, are particularly easy to set up when collapse and other (blue) specifying folded native-like configurations. The same non-specific secondary structure formation precede the transition-state ensemble (green) as in Figure 1 is represented in this rate-limiting stages of folding. A multidimensional funnel lower dimensional view. The height of the thermodynamic barrier is approximately 2kBTf= 1.2 kcal mol-t. picture that includes additional energy scales for other 428 Chemistry & Biology 1996, Vol3 No 6
molecule such as extensive sequence and solvent changes folded and transition-state ensembles, respectively. F that lead to the same stability give a similar shaped funnel. global perturbations, @ gives a good first approximation If the corresponding-states approach were not valid, simu- the position of this bottleneck. @ will be strongly con lations of minimalist models could only be used as sugges- lated to the degree of nativeness of the transition-St2 tive analogies to laboratory protein folding. Thus, this ensemble. Only an average description is obtains experiment encourages the application of landscape however, using a single value of CD.Proteins are polyme theory and simulations as quantitative tools. leading to varying participation of different residues in t transition-state ensemble, and protein engineering tee Depending on the quantitative variation of entropy, mean niques reveal a histogram of participation of residues energy and ruggedness as the protein ensemble descends the configurations of a transition state ensemble, center’ in the funnel, energy-landscape theory provides a classifi- around a fractional value ([Zl] and J.N.O., P.G.W., 2.L.. cation of kinetic scenarios [Z]. If the energy loss always & N.D. Socci, unpublished data). Of course, as increase exceeds the entropy, we have a type 0 or ‘downhill’ stabilization can transform a type I scenario to a downh folding scenario. Downhill folding on a relatively smooth one, some curvature of the LFER is also to be expected. landscape would resemble the physical process of polymer collapse and would not be expected to follow the simple Type II scenarios occur if the ruggedness of the landsca exponential kinetics of a first order chemical reaction. For is very large, so that only a few discrete trap configuratio rougher landscapes, downhill processes would have an can be thermally occupied, even before the bottleneck even wider distribution of time scales because of the kinetically surmounted (type IIB). This transition to d varying depths of traps. These signatures should be quite Crete long-lived traps in the type IIB scenario has much obvious in fast folding experiments. For the roughest common with the glass transition, where disordered confi landscapes, only a few discrete traps could be populated urations of a liquid can exist for long periods of tin and the dynamics could be described by a discrete but Although the rough location of transition to this regime c complex kinetic scheme, after the resolution of the early be inferred from simple statistical mechanical theori events. A different result is seen when the rate of energy involving the interplay of ruggedness and entropy, t loss down the funnel does not match, at each stage, the most important result of landscape theory for the kinetic entropy loss as the ensemble descends. As the free energy is the prediction that the existence of each specific trap is defined as E - TS, a free energy maximum will result very sensitive to even single-site changes in the molect when the entropy decreases more rapidly than the energy. and might be eliminated by simple protein engineering 1 In this type I scenario, a bottleneck occurs in the folding sometimes, by chemistry [17,33]. Many of the classica process. The ensemble of structures at the bottleneck rep- studied folding processes encountered type II scenari resents a free energy barrier, and at the macroscopic level either after a downhill run or after encountering an esI the folding can be described using single-step, exponen- cially small entropic barrier at the bottleneck ensemb tial kinetics. Landscape theory predicts simple regularities Landscape theory for type II folding can only be test’ for the folding-rate coefficient when the type I scenario quantitatively with combinatorial experiments testing t applies. As a large number of different configurations are distribution of intermediate lifetimes using a variety of d present at the bottleneck, detailed energetic effects on ferent sequences. The fast folding events, on the otl- single configurations get averaged out, and thus the hand, should conform to type 0 or type I scenarios a folding rate is largely and smoothly related to the stability. therefore will exhibit greater regularities and be dominat by the guiding forces for folding rather than ruggedne Transfer coefficients (@) in local linear free energy rela- and trapping. tions (LFER) reflect the location of the bottleneck ensem- ble along the reaction coordinate. Using the assumption Fast folding experiments to date that bottleneck position does not change much when the To initiate fast folding, the protein in question mr landscape is changed, we can derive an LFER between somehow be converted, almost instantaneously, from the folding time, rf, and the free-energy change in folding, form that favors the unfolded state to a form that favc which to the same order is < AH >21- 4 AH >f (J.N.O., the folded state. Several methods have recently be P.G.W., Z.L.-S. & N.D. Socci, unpublished data), where developed to trigger this event. The first protein to the brackets indicate averaging over an ensemble. Thus: explicitly studied on the fast (submillisecond) time SC: was cytochrome C, in an effort led by Eaton and Rot cAH>~~-
to misassociate with the heme iron, leading to a kinetic Figure 5 trap [33]. Jones et al. [9] initiated folding photochemi- tally by exploiting the fact that the stability of the protein is enhanced by coordination with two sidechains of the polypeptide chain. Cytochrome c with bound carbon monoxide thus denatures more readily than the protein that lacks CO, and flash photolysis of the CO- bound form with a laser can initiate folding within pico- seconds under appropriate denaturing conditions. The change in stability is modest, so the experiment must be performed with a relatively high denaturant concentra- tion to ensure that the initial CO-bound form is com- pletely denatured. This procedure leads to type I folding in about 10 ms. Significantly, Jones et all also observe complex spectral changes, beginning in the microsecond range. These relaxation events occur exclusively in the unfolded phase, but unfortunately all the free energy gradient in this case is caused by the differing chemical stability of the amino acids in the chain that can act as ligands of the heme and not by the dominant folding forces.- Nevertheless combining these measurements of the dynamics in the unfolded state with a separate deter- mination of the inherent chemical effects on ligand asso- A composite picture is shown of the sample cell and laser T-jump ciation has led to a plausible upper limit on the speed of apparatus of Ballew et a/. [13] that was used to measure the folding of apomyoglobin from its cold-denatured state and the computer downhill protein folding of 1 ks [34]. simulations of two conformations with a low (top) and high (bottom) fraction of native contacts. The conformations were obtained from a Gray and colleagues [l&23] exploit a conceptually similar protein structure prediction simulation using an associative memory route to fast folding. Reduced and oxidized cytochromes energy function 1391 and are color-coded to indicate the foldon regions have different stabilities, and at a particular concentration [351 that could be kinetically competent quasi-independent folding units. of denaturant, the oxidized protein is unfolded and the reduced protein is folded. Thus photo-initiated electron transfer can induce folding. The oxidized, unfolded concentration. This is true even though the sequences protein is bombarded with electrons, and upon conversion are only 50 % identical. This non-sequence-specificity to the reduced form, folding is instantly favored. Using a of type I funnel-like folding contrasts greatly with the photosensitizer electron injection system, they were able dynamics of type II folding; for example, the late-stage to initiate folding in less than 1 p,s [la]. As the reduced folding intermediates of lactalbumin and hen lysozyme cytochrome c in this case had a lifetime of only - 1 ms, a dif- are quite different [18]. This is true despite the fact that ferent injection system was used to study longer periods of the two proteins share 36 % sequence identity. time. Although it causes a larger stability change than CO binding, the electron transfer initiated folding was still Laser fast folding experiments can examine the dynamics studied under type I scenario conditions, giving results of a larger portion of the folding events only by obtaining consistent with the earlier work, while reducing some tech- bigger stability changes. This can be achieved with a nical difficulties arising from back reactions. T-jump. The record for initiating folding thus far has been achieved in groundbreaking experiments of Gruebele and The experiment described in this issue by Mines et al colleagues [13], schematically presented in Figure 5. [23] also uses electron-transfer triggering to show a Laser heating using an infrared pulse allows a protein that remarkable regularity that is expected for type I transi- is denatured because of the cold to be taken to conditions tions. The part of the folding funnel probed in a type I that favor the native form within nanoseconds. scenario is predicted to be self-averaging, so two quite different sequences folding to the same structure should This technique to has been applied to the study of have funnel shapes in the region of high density of states apomyoglobin, which is denatured by cold at a convenient (above the transition states) that depend mostly on the temperature near the freezing point of water. Conform- overall stability and amino-acid composition of the mol- ational changes can then be monitored by measuring ecule. The experiments of Mines et al. show that horse fluorescence decay of the tryptophan by repetitive femto- and yeast cytochrome c have the same folding rates when second pulses after initiating folding. Modeling the fluor- tuned to the same stability by adjusting the denaturant escence decays at equilibrium leads to the conclusion that 430 Chemistry & Biology 1996, Vol3 No 6
the change that is detected between native and non-native Although most of the action in fast folding seems to occur states is primarily determined by a specific contact between in the range of microseconds, very fast processes have also a methionine and the tryptophan. Thus the experiment been observed in unfolding experiments, such as those measures part of the tertiary structural transition. The data examining the thermally induced unfolding of apomyo- can be fit by a largely exponential process, indicating a type globin [ll]. Protein conformation is probe using vibra- I scenario for this conformational change, which occurs in tional spectroscopy techniques that ared\ sensitive to 7 ps. There are also some signs of shorter time scale secondary structural changes. Interestingly, if the process changes in the decay, which may be connected with sec- is two-state, one of the fast unfolding processes observed ondary structure formation or more local collapse of the could be interpreted to give a refolding time constant polypeptide chain. The assignment of the major spectral close to that determined by laser heating, if the tempera- change to a large-scale conformational movement is sug- ture dependence of viscosity is taken into account. Tran- gested by its viscosity dependence, as shown by adding sient infrared spectroscopy has also been used by monitor glycerol to the solution. This study confirms a Kramers-like events occurring in nanosecond timescales [lo]. These dependence of the rate on external viscosity [31]. Longer experiments show fairly complicated kinetics that cannot time scale measurements show that the transition seen by be fit by a single-step representation. Some changes occur Gruebele and coworkers is not complete folding [19]. At on such short timescales that they may be accessible to least in sperm whale apomyoglobin, the complete folding direct molecular dynamics simulation [37]. Clearly a rich occurs later. This may suggest the presence of a subdomain variety of phenomenology is beginning to appear from the structure in the apomyoglobin molecule or specific traps submillisecond folding experiments. While many inter- during folding [35]. pretational questions remain to be answered, it is quite clear that events that were earlier postulated based only The observations of interesting dynamics on the micro- on slow stopped-flow mixing experiments were just a second timescale with cytochrome c and apomyoglobin are small part of what is going on. also confirmed in a fast T-jump experiment on barstar (barnase inhibitor) [36]. A rapid transition taking 300 ps Quantifying funnel shapes with fast-folding experiments is followed by a lOO-ms slow phase. The rapid change We are just beginning to understand protein folding quan- involves a very small amplitude of fluorescence change but titatively in terms of energy-landscape topography. The is clearly not an artifact. As in the experiments with cyto- fast-folding experiments we have just discussed support chrome c [23], the location of the transition state (Q) for the qualitative notions of the theory and begin to allow us this folding is early along the folding reaction coordinate as to refine the quantitative aspects of the funnel shape. judged by its denaturant dependence. Clearly many inter- Foremost among the issues in funnel shape are the ques- esting folding processes occur on the microsecond to milli- tions of the appropriate coordinates for describing the second timescale. These processes can also be observed crucial, partially folded ensembles of structures. In the using an enhancement of the conventional mixing tech- simplest model, the fraction of native contacts (Q) is used. niques using small orifices. One such ultrafast mixing Because each experiment has so far used only a small frac- experiment with cytochrome c shows a folding process that tion of the possible probes, this very basic issue still is strongly extended and nonexponential, suggesting the requires much study. Clearly the important configurations, possibility of a downhill or type 0 folding scenario [ZO]. This as revealed in these experiments, are partially collapsed novel technique is still in its early stages and several com- and probably have some secondary structure formed, and plexities concerning the interaction of the turbulent hydro- even though parts of the secondary structure may be in dynamic flows and the polymer conformations need to be the correct locations, only a small amount of tertiary order- sorted out in order to be completely confident of the ing may exist. Many of the next generation of experiments results. Notice here that there is an apparent change of the will begin to address these issues more completely using @ values, suggesting that nonlinearity of the free energy other techniques. Circular dichroism would be a more con- relation can be observed when experiments are done over a vincing measure of overall secondary structure, while iso- large enough range of denaturant concentrations. topic labeling and vibrational spectroscopy could locate the precise secondary structural elements [ 111. NMR spectral line shape analysis can be used, at least near the midpoint of the folding curve, to study submillisecond More refined fluorescence experiments using mutants with folding dynamics. This technique has been used to exam- tryptophan residues placed in varying locations could pin- ine both folding and unfolding of monomeric X repressor point tertiary contacts. Even without the precise definition [14]. This molecule is highly helical and closely resembles of the relevant coordinates, some quantitative features - many of the systems studied by the theoreticians. Again an the entropic aspects of the landscape and the ruggedness intermediate 4, value is observed showing the existence - are grossly revealed by the experiments to date and of a bottleneck or a transition state ensemble in a type I seem to have a reasonable relationship to the theoretical scenario near to the location predicted from theory. expectations. The fast folding experiments all suggest that Review Fast folding Wolynes et a/, 431
the bottleneck for folding at the midpoint of the denatur- the early part of this review should apply for the smaller ing curve corresponds to a transition state ensemble with a protein systems. The experiments with apomyoglobin considerable configurational entropy. The fractional degree suggest that a unit consisting of the A, G and H helices of folding as determined from linear free-energy relation- forms first. This unit is similar to the size of proteins ships agrees reasonably well with results obtained from described by a single funnel but clearly the overall folding lattice simulations as expected from the corresponding may require a funnel for each substructure. A theoretical states principle interpretation of the funnel landscape. description of folding in domains or foldons has already This is probably the best current measure of the entropic been made using energy-landscape analysis [35]. effects in the funnel. More detailed studies of the specific contacts formed in the transition state ensemble are also in Fast folding experiments provide the most direct view agreement with the picture that a collection of delocalized on the forces that govern the self-organization of pro- folding nuclei are important. tein molecules. The quantification of energy-landscape topography that these experiments will make possible The ruggedness of the landscape can be quantified more should help structure prediction schemes that are already accurately using the temperature dependence of the based on landscape ideas, but which have been handi- folding rate when under type I conditions or by the capped by only knowing the final folded structures of detailed time course in a type 0 downhill folding scenario. proteins. Thus, we can look forward to a very fruitful The data from the cytochrome c experiments show that interaction between the experimental community and configurational diffusion is faster at high temperatures the computational community. than at low, as the isostability values of the folding rate are higher at 40 “C than at 22.5 “C [l&23]. Some of this effect Acknowledgements can be attributed to the change in viscosity with tempera- The work at the University of California at San Diego was supported by the ture, as would be expected from the experiments with NSF (Grant No. MCB-93-16186) and at Illinois by the NIH (Grant No. 2 ROI GM44557). apomyoglobin [ 131, but this would only account for a small fraction of the effect. The ratios of the viscosity at these References two temperatures is -1.5, but the rate ratio is -20. We are 1. Kim, P.S. & Baldwin, R.L. (1990). Intermediates in the folding only able to calculate a value for the apparent activation reactions of small proteins. Annu. Rev. Biochem. 59, 631-660. barrier by assuming that the entire ruggedness is enthalpic 2. Bryngelson, J.D., Onuchic, J.N., Socci, N.D., & Wolynes, P.G. (1995). Funnels, pathways and the energy landscape of protein folding: a (whereas it is doubtless partially entropic due to the synthesis. Proteins 21, 167-l 95. hydrophobic effects); nevertheless, with this imperfect 3. Friedrichs, M. & Wolynes, P.G. (1990). Molecular dynamics of description we arrive at a value of E, - 1 lkBTY We should associative memory Hamiltonians for protein tertiary structure recognition. Tetrahedron (Camp. Mefh) 3, 175-l 90. be very careful when providing an interpretation of such 4. Dill, K.A., et a/., & Chan, H.S. (1995). Principles of protein folding: a an apparent barrier [27,31]. The simplest description, perspective from simple exact models. Protein Sci 4, 561-602. 5. Honevcutt, J.D. & Thirumalai. D. (1992). The nature of the folded state using the configurational diffusion model of Bryngelson of gldbular proteins. Biopolymer$32, 695-709. and Wolynes [27], directly relates this barrier to the 6. Sali. A., Shakhnovich. E. & Karolus. M. (1994). Kinetics of orotein average roughness of the landscape. According to their folding: a lattice model study df the requirements for foldin’g to the native state. J. Mol. Biol. 235, 1614-l 636. model, at temperatures sufficiently high compared to the 7. Socci, N.D. & Onuchic, J.N. (1994). Folding kinetics of protein-like glass transition temperature, E, - AE2/2k,Tf = 10kBTf heteropolymers. J. Chem. Phys. 101, 1519-I 528. Below the glass transition temperature, the system 8. Socci, N.D. & Onuchic, J.N. (1995). Kinetic and thermodynamic analysis of protein-like heteropolymers: Monte Carlo histogram becomes caught in a few long-lived non-native states, technique. J. Chem. Pbys. 103,4732-4744. making the average ruggedness description invalid. The 9. Jones, C.M., et a/., & Eaton, W.A. (1993). Fast events in protein folding initiated by nanosecond laser photolysis. Proc. AM Aced. SC;. experimental value obtained for this apparent barrier is lJSA90,11860-11864. slightly larger than the actual simulated value, E, - 7kBTi, IO. Phillips, CM., Mizutani, Y. & Hochstrasser, R.M. (1995). Ultrafast using the corresponding-state analysis for a 60 residue thermally induced unfolding of RNase A. Proc. Nat/. Acad. Sci. USA 92, 7292-7296. protein. Estimates of the ruggedness and conformational 11. Williams, S., et a/., & Dyer, R.B. (1996). Fast events in protein folding, diffusion activation barriers can be refined by much more helix melting and formation in a small peptide. Biochemistry 36, extensive studies in a larger temperature and viscosity 691-698. 12. Pascher, T., Chesick, J.P., Winkler. J.R. & Grav. H.B. (1996). Protein range, both for the data of Mines et aL [23] with a type I folding triggered by electron transfer. 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